Operational Amplifiers
Outline
Introduction
 Background
 Fundamentals of Op-Amps
 Real vs. Ideal
 Applications

What is an Op-Amp

Low cost integrating circuit consisting of
 Transistors
 Diodes
 resistors
 capacitors

Op-amps amplify an input signal using an
external power supply
Uses for Op-Amps


Op-Amps are commonly used for both linear and
nonlinear applications
Linear
 Amplifiers
 Summers
 Integrators
 Differentiators
 Filters

(High, Low, and Band Pass)
Non-linear
 Comparators
 A/D
converters
Vacuum Tube Op-Amps

First op amps built in 1930’s1940’s
 Technically
feedback amplifiers
due to only having one useable
input

Used in WWII to help how to
strike military targets
 Buffers,
summers, differentiators,
inverters

Took ±300V to ± 100V to power
http://en.wikipedia.org/wiki/Image:K2-w_vaccuum_tube_op-amp.jpg1
Solid State Discrete Op-Amps

Solid state op amps invented in
1960’s
 Possible
due to invention of
silicon transistors and the IC
 Chip and discrete parts
Reduced power input to ±15V
to ±10V
 Packaging in small black boxes
allowed for integration with a
circuit

Monolithic Integrated Circuit Op-Amp

First created in 1963
 μA702

by Fairchild Semiconductor
μA741 created in 1968
 Became
widely used due to its
ease of use
 8 pin, dual in-line package (DIP)

Further advancements include
use of field effects transistors
(FET), greater precision, faster
response, and smaller packaging
Features of Op-Amps







+Vin: non-inverting input
+Vin
-Vin: inverting input
+Vs: positive source
-Vin
-Vs: negative source
Vout: output voltage
ON: Offset Null
ON
NC: Not Connected
+Vs
+
Vout
-
-Vs
-Vin
NC
+Vs
+Vin
Vout
-Vs
ON
Characteristics of Op-Amps
Ideal Op-Amp

Infinite open loop gain
(GOL):
 Zero

Real Op-Amp

 Decreases
with increase
in frequency
 Non-zero common mode
gain
common mode gain
Infinite bandwidth:
 Range
of frequencies
with non-zero gain
Limited open loop gain:

Limited Bandwidth:
 Gain
becomes zero at
high frequencies
Characteristics of Op-Amps
Ideal Op-Amp
Real Op-Amp

Infinite slew rate

Finite slew rate

Infinite input impedance

Large input impedance
 No

 Small
input current
Zero output impedance
 Infinite
output current

input current
Non-zero output
impedance
 Limited
output current
The open-loop gain of an operational amplifier is the gain
obtained when no feedback is used in the circuit. Open loop
gain is usually exceedingly high; in fact, an ideal operational
amplifier has infinite open-loop gain.
The slew rate of an electronic circuit is defined as the
maximum rate of change of the output voltage. Slew rate is
usually expressed in units of V/µs
An ideal op-amp is usually considered to have the following properties, and they are
considered to hold for all input voltages:
1. Infinite open-loop gain (when doing theoretical analysis, a limit may be taken as open
loop gain AOL goes to infinity).
2. Infinite voltage range available at the output () (in practice the voltages available from
the output are limited by the supply voltages and ). The power supply sources are
called rails.
3. Infinite bandwidth (i.e., the frequency magnitude response is considered to be flat
everywhere with zero phase shift).
4. Infinite input impedance (so, in the diagram, , and zero current flows from to ).
5. Zero input current (i.e., there is assumed to be no leakage or bias current into the
device).
6. Zero input offset voltage (i.e., when the input terminals are shorted so that , the output
is a virtual ground or ).
7. Infinite slew rate (i.e., the rate of change of the output voltage is unbounded) and
power bandwidth (full output voltage and current available at all frequencies).
8. Zero output impedance (i.e., , so that output voltage does not vary with output current).
9. Zero noise.
10. Infinite Common-mode rejection ratio (CMRR).
11. Infinite Power supply rejection ratio for both power supply rails.
These ideals can be summarized by the two "golden rules":
1. The output attempts to do whatever is necessary to make
the voltage difference between the inputs zero.
2. The inputs draw no current.
The first rule only applies in the usual case where the op-amp is
used in a closed-loop design (negative feedback, where there is a
signal path of some sort feeding back from the output to the
inverting input). These rules are commonly used as a good first
approximation for analyzing or designing op-amp circuits.
Summary of Characteristics
Parameter
Ideal Op-Amp Typical Op-Amp
GOL
∞
105 - 109
Common Mode
Gain
Bandwidth
0
10-5
∞
1-20 MHz
Input
Impedance
∞
106 Ω (bipolar)
109-1012 Ω (FET)
Output
Impedance
0
100-1000 Ω
Ideal Op-Amp




Active device
Infinite open loop gain
Infinite input impedance
Zero output impedance
+Vs
iin = 0A
+
Vdiff
Vout = Vdiff x Gopenloop
-Vs
Negative Feedback

Vout is a linear function of the input voltage

Zin = infinity

Modelisation of basic mathematical
operation
Iin=0A
Vdiff=0V
Non Inverting Circuit
iin = 0A
Vin
+Vs
(1) V- - Vout = R2 x i
+
Vout
Vdiff = 0V
0A
R1
V- = V+ = Vin
-Vs
i
(2)
i = -Vin/R1
R2
(1)
V-
(2) V- = - R1 x i
Vin – Vout = -Vin x R1/R2
V- - Vout
Vout = (1 + R1/R2) x Vin
Inverting Circuit
+Vs
iin = 0A
(1) V- - Vout = R2 x i
+
Vout
Vdiff = 0V
(2) Vin - V- = R1 x i
-Vs
Vin
R1
Vin – V-
i
R2
V- - Vout
V- = V+ = 0
(1)
i = Vin / R1
Vout = - R2/R1 x Vin
Follower Circuit
- Vs
Summing Op-Amp
• Adds analog signals
Ohm’s Law:
Solving for Vout:
V1  V V2  V V3  V V  Vout



R1
R2
R3
Rf
 V1 V2 V3 
Vout   R f  
 
 R1 R2 R3 
Summing Op-Amp
Difference Op-Amps
• Subtracts analog signals
• Output voltage is proportional to
difference between input voltages:
Vout

R3  R1 R4

V
R3
V1
2 
( R4  R2 ) R1
R1
Difference Op-Amp
Integrator Op-Amps
•Similar layout to inverting op-amp,
but replace feedback resistor with
a capacitor
•A constant input signal generates
a certain rate of change in output
voltage
• Smoothes signals over time
•Output voltage is proportional to
the integral of the input voltage:
t
1
Vout, final  Vout,initial  
Vin dt

RC 0
Integrator Op-Amp
Differentiating Op-Amp
•Similar to inverting op-amp, but
input resistor is replaced with a
capacitor
•Accentuates noise over time
• Output signal is scaled
derivative of input signal:
dVin
Vout   RC
dt
Differentiating Op-Amp
Active Filters

Different types of active filters:
 Low

Pass
Filters out frequencies above a cutoff frequency
 High

Filters out frequencies below a cutoff frequency
 Band

Pass
Pass
Passes a range of frequencies between two cutoff
frequencies
Active Low-Pass Filter

Cutoff frequency:
1
c 
R2C
Active High-Pass Filter

Switch positioning of capacitors and resistors from lowpass filter locations to create high-pass filter.
Active Band-Pass Filter


Created by connecting output of a highpass filter to the input of a low-pass filter or
vice versa.
Also can create using only 1 op-amp with
feedback and input capacitors
No negative feedback

Vout is a non-linear function of the differential
input voltage V+ - V-

V+ - V- = Vdiff

Vout = sign(Vdiff) x Vs

Binary logic and oscillator
Comparator
Vout ( volts )
+Vs
iin = 0A
+
Vout
Vdiff
+ Vs
-
V+
Vdiff
0V
V-
-Vs
- Vs
Comparator
Common-Mode Input Resistance (RINCM)
For op amps operating in the linear region, this term defines the input
common-mode voltage range divided by the change in input bias current
across that range.
2. DC Common-Mode Rejection (CMRDC)
This is a measure of the op amp's ability to reject DC signals present in
equal measure at both inputs.
CMRDC can be calculated using the common-mode voltage range (CMVR)
and the change in peak-topeak input offset voltage across that range.
References




“Operational Amplifiers.”
http://en.wikipedia.org/wiki/Op_amp
“Real vs. Ideal Op Amp.”
http://hyperphysics.phyastr.gsu.edu/hbase/electronic/opamp.html#c4
“741 Op Amp Tutorial.”
http://www.uoguelph.ca/~antoon/gadgets/741/74
1.html
“Op Amp History.” Analog Devices.
http://www.analog.com/library/analogDialogue/ar
chives/39-05/Web_ChH_final.pdf